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nataly862011 [7]

2 years ago

15

Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all

ergic to penicillin, Nathan had a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is allergic to penicillin and the test predicts it?

2 answers:

Basile [38]2 years ago

7 0

Answer:

0.735

Step-by-step explanation:

Let A be the event of being allergic to penicillin and T be the event that the test predicted the allergy is accurate.

According to the question,

There is 75% chance of having the allergy.

⇒ Probability of being allergic to penicillin, P(A) = 75 % = 0.75,

Also, the test is 98% accurate.

⇒ Probability that the allergy is predicted by the test, P(B) = 98% = 0.98

Since, both A and T are independent events,

Thus, the probability that Nathan is allergic to penicillin and the test predicts it

= P(A) × P(T)

= 0.75 × 0.98

= 0.735

Gwar [14]2 years ago

3 0

There is a 73.5% chance that Nathan is allergic to penicillin and the test predicts it.

75% * 98% = 73.5%

.75 * .98 = .735

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